Rendering Wada-type basins of attraction
Here's a party trick for over Christmas. Get 4 large shiny Christmas balls,
some coloured wrapping paper, some lights from the Christmas tree,
and you have you own fractal laboratory to amuse yourself with over
the festive season.

I wonder whether fractal images are not touching the very structure of our
brains. Is there a clue in the infinitely regressing character of such images
that illuminates our perception of art? Could it be that a fractal image is
of such extraordinary richness, that it is bound to resonate with our neuronal
circuits and stimulate the pleasure I infer we all feel?
P. W. Atkins

NoiseIncluding 1/f noise. Fractal planets and landscapes:
Methods for creating fractal planets, landscapes, and clouds.
Generating noise with different power spectra laws.
Including frequency synthesis and midpoint displacement and a
gallery of images created using Voxel World by Dmytry Lavrov.
Perlin noise and turbulence: Creating arbitrary dimensional textures
and other natural effects using techniques credited to Ken Perlin.

The Pale Blue Dot from Space - Earth.
"That's here. That's home. That's us. On it everyone you love,
everyone you know, everyone you ever heard of, every human being
who ever was, lived out their lives. The aggregate of our joy and
suffering, thousands of confident religions, ideologies and economic
doctrines, every hunter and forager, every hero and coward,
every creator and destroyer of civilization, every king and peasant,
every young couple in love, every mother and father, hopeful child,
inventor and explorer, every teacher of morals, every corrupt
politician, every superstar, every supreme leader, every saint and
sinner in the history of our species lived there - on a mote of
dust suspended in a sunbeam." Carl Sagan

"And are you not", said Fook leaning anxiously forward, "a greater analyst
than the Googleplex Star Thinker in the Seventh Galaxy of Light and Ingenuity
which can calculate the trajectory of every single dust particle
throughout a five-week Dangrabad Beta sand blizzard?"
"A five-week sand blizzard?" said Deep Thought haughtily. "You ask this of me
who have contemplated the very vectors of the atoms in the Big Bang itself?
Molest me not with this pocket calculator stuff."
Douglas Adams

I am so in favour of the actual infinite that instead of admitting that
Nature abhors it, as is commonly said, I hold that Nature makes
frequent use of it everywhere, in order to show more effectively
the perfections of its Author. Georg Cantor

Is the human story largely a deterministic tale of civilisations
marching to Toynbee's tune, three and a half beats to disintegration,
or did the hinge of history turn on the length of Cleopatra's nose?
Robert May

The real world was full of larger structures, smaller structures,
simpler and more complex structures than the tiny portion comprising
sentient creatures and their societies, and it required a profound
myopia of scale and similarity to believe that everything beyond this
shallow layer could be ignored.
Greg Egan, Diaspora